Consider a ring of mass \(m\) and radius \(R\) touching a rough wall of coefficient of friction \(\mu\) as shown in figure. The ring has an initial angular velocity of \(\omega_0\).
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Find the time taken by the ring to come to a halt.

**Details and Assumptions**

The ring doesn't translate on the wall.

\(\mu = \dfrac{1}{\sqrt{3}} \)

\(m = 1 kg\)

\(R = 1 m\)

\(\alpha = \dfrac{\pi}{3}\)

\(\omega_0 = 10 rad/s\)

\(g = 10 m/s^2 \)

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